| Single molecule microscopy is a powerful technique for investigating biological processes at the level of individual molecules. In this technique, individual molecules are detected via their fluorescence, which is typically recorded using a charge-coupled device-based (CCD-based) camera. In this thesis, contributions are made to the analysis of these camera-detected images.;In terms of Fisher information, the contribution is twofold. First, a Cramer-Rao lower bound-based three-dimensional (3D) resolution measure is proposed which specifies the best accuracy with which the distance separating two molecules in 3D space can be estimated from CCD-acquired images. This is relevant to the study of biomolecular interactions, since an accurately determined separation distance helps to characterize the interaction between two molecules. The 3D resolution measure importantly predicts that, using a conventional microscope, arbitrarily small distances can be estimated with prespecified accuracy. However, since the required photon count is often unattainable, the resolution measures for several non-conventional microscopy setups are derived and, given a limited photon count, shown to be superior to that for the conventional microscope. Second, Fisher information expressions are derived for parameter estimation on images acquired using an electron-multiplying CCD (EMCCD) camera. Due to its ability to amplify a weak signal above the level of its own measurement noise, the EMCCD typically replaces the CCD when few photons can be detected from the single molecules. The signal amplification is stochastic, and is modeled here as a geometrically multiplied branching process. Exact and approximate Fisher information expressions are derived which allow the computation of Cramer-Rao lower bounds for specific estimation problems.;In terms of software, the Microscopy Image Analysis Tool (MIATool) software framework is proposed which provides high level support for the analysis of multidimensional and potentially large image data sets. Central to this framework is the idea that different analysis tasks are often facilitated by different arrangements of the images in a data set. MIATool thus uses arrays of image pointers to efficiently realize logical image arrangements of arbitrary dimensionality and size. The small size of a pointer compared to its referenced image also naturally allows MIATool to accommodate the analysis of large data sets. |
